Calculus: 1001 Practice Problems For Dummies (+ Free Online Practice). Patrick Jones

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Adding Polynomials

       83–87 Add the given polynomials.

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Subtracting Polynomials

       88–92 Subtract the given polynomials.

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Multiplying Polynomials

       93–97 Multiply the given polynomials.

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Long Division of Polynomials

       98–102 Use polynomial long division to divide.

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Chapter 2

      Trigonometry Review

      In addition to having a strong algebra background, you need a strong trigonometry skill set for calculus. You want to know the graphs of the trigonometric functions and to be able to evaluate trigonometric functions quickly. Many calculus problems require one or more trigonometric identities, so make sure you have more than a few of them memorized or at least can derive them quickly.

The Problems You’ll Work On

      In this chapter, you solve a variety of fundamental trigonometric problems that cover topics such as the following:

       Understanding the trigonometric functions in relation to right triangles

       Finding degree and radian measure

       Finding angles on the unit circle

       Proving identities

       Finding the amplitude, period, and phase shift of a periodic function

       Working with inverse trigonometric functions

       Solving trigonometric equations with and without using inverses

What to Watch Out For

      Remember the following when working on the trigonometry review questions:

       Being able to evaluate the trigonometric functions at common angles is very important since they appear often in problems. Having them memorized will be extremely useful!

       Watch out when solving equations using inverse trigonometric functions. Calculators give only a single solution to the equation, but the equation may have many more (sometimes infinitely many solutions), depending on the given interval. Thinking about solutions on the unit circle is often a good way to visualize the other solutions.

       Although you may be most familiar with using degrees to measure angles, radians are used almost exclusively in calculus, so learn to love radian measure.

       Memorizing many trigonometric identities is a good idea because they appear often in calculus problems.

Basic Trigonometry

      103–104 Evaluate , , and for the given right triangle. Remember to rationalize denominators that contain radicals.

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       105–108 Evaluate the trig function. Remember to rationalize denominators that contain radicals.

      105. Given , where , find .

      106. Given , where , find